I've learned that the answer to so many questions posted on Scubaboard are most accurately answered with, "It depends." No way to get around that...
As others have mentioned, much of what "depends" in your question is your tolerance to cold, the temperatures you'll most likely be diving in, and what level of activity do your dives entail.
Your budget is also a major consideration--also a very accurate "correct" answer to Scubaboard questions. If your temperature tolerance is low and your budget toleralance is high, then the "correct" answer is simple--buy a dry-suit.
However, I suspect as you have excluded drysuits from your question, your budget is a key consideration--welcome to the club.
With all of this said, here is my 2 psi... I found the "perfect" (at least for me) first wet-suit was a 5mm and then layer as appropriate for the conditions. By layering a 5/3 hooded vest underneath, I could dive semi-comfortably at the bottom of our local quarry at 49 degrees. However, I have also dove just the 5mm suit in Hawaii and off of North Carolina waters which were between 79-81 degrees without any risk of overheating. In fact, I found the suit wasn't "too warm" even the heated indoor pool in our area.
For what it's worth...
Jan